Participants in the first Egyptian vote of the post-Morsi era have voted overwhelmingly in favour of approving a new constitution.

More than 90% of voters opted to ratify Egypt's third constitution in as many years, state-run media reported – a result likely to be portrayed by the Egyptian establishment as a conclusive endorsement of the direction the country has taken since the overthrow of Mohamed Morsi.

But after a campaign in which no campaigners were arrested and the government said participation was a patriotic duty, many also saw the poll's turnout as a more significant indicator of public sentiment.

Provisional results suggested turnout was just over 38% – higher than the 33% who voted in a referendum during Morsi's tenure, but lower than the 41.9% who turned out in a similar poll following Egypt's 2011 uprising.

Egypt's new constitution strengthens the country's three key institutions – the military, the police and the judiciary – as well as removing certain Islamist-leaning clauses inserted under Morsi, and gives more rights to women and disabled people.

But the referendum was seen less as a poll on the text's contents and more of a vote on Egypt's current leadership.

In the buildup to the poll, General Abdel Fatah al-Sisi, the army chief who ousted Morsi last July, hinted he would view a strong yes vote and a high turnout as a mandate to run for the presidency later this year.

Shortly before polls closed on Wednesday, the army's spokesman, Ahmed Ali, appeared to position the referendum as an endorsement of Egypt's new order.

Egyptians, he was quoted as saying, were "the first free people in the history of humankind, [and] have continued to surprise the world by working to build a modern future".

Pro-army sentiment was clearly displayed in many polling stations, with supporters of the process circulating several photographs of women kissing soldiers policing voting queues. In one polling station, a stereo played a pro-army song so loudly that those present could not hear each other speak.

As the final hours of polling approached, one television channel split its screen into 16 sections to display 16 different polling queues, in an attempt to exaggerate the extent of voter turnout. Others said voting yes was a revolutionary act essential to the country's future. "You built the pyramids," talkshow host Tawfiq Okasha reportedly told his viewers following the end of polling, "and today you built the future for all of humanity."

Enthusiasm for the poll seemed to contrast sharply between the country's north and south. In upper (or southern) Egypt, turnout was noticeably down from 2012, whereas the opposite largely held true in the north.

The south has traditionally been a stronghold for Islamist groups, who almost all boycotted the poll in protest at Morsi's overthrow and at a crackdown on Islamist dissent.

The referendum's integrity has been challenged by opposition members and rights campaigners, who say the poll was conducted against a backdrop of fear. Up to 35 no campaigners were arrested, claimed one opposition party that boycotted the poll in protest. Their arrests follow the jailing of thousands of Islamists, as well as dozens of secular activists, since last July.